The differential decay rate for is given by
The Dalitz plot density
is a Lorentz invariant function which contains in the
following form,
with
The quantities are related to the ones quoted by the PDG [3]
by
To obtain the rate for , one replaces in (3.17)
by
.
For convenience we also display the rates evaluated in the
approximation (3.8) for the form factors,
We have used the physical masses [3] in evaluating these ratios and
to scale the slope in both cases. The
terms linear and quadratic in
are proportional to
and
therefore strongly suppressed in the
electron case. We do not include them in the denominators,
because these coefficients
are smaller than
. The interference term
is
absent by angular momentum conservation.
Furthermore, one has